A020927 Expansion of (1-4*x)^(15/2).

1, -30, 390, -2860, 12870, -36036, 60060, -51480, 12870, 2860, 1716, 1560, 1820, 2520, 3960, 6864, 12870, 25740, 54340, 120120, 276276, 657800, 1614600, 4071600, 10518300, 27768312, 74760840, 204900080, 570793080, 1613966640, 4626704368, 13432367520

Offset

0,2

Links

Table of n, a(n) for n=0..31.

Formula

D-finite with recurrence: n*a(n) +2*(-2*n+17)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

From Amiram Eldar, Mar 25 2022: (Start)

a(n) = (-4)^n*binomial(15/2, n).

Sum_{n>=0} 1/a(n) = 972/1001 + 34*Pi/(3^10*sqrt(3)).

Sum_{n>=0} (-1)^n/a(n) = 18235778692/17595703125 - 68*log(phi)/(5^9*sqrt(5)), where phi is the golden ratio (A001622). (End)

Mathematica

CoefficientList[Series[(1-4x)^(15/2), {x, 0, 30}], x] (* Harvey P. Dale, Oct 03 2012 *)

Crossrefs

Cf. A001622, A002420, A002421, A002422, A002423, A002424, A020923, A020925, A020929.

Sequence in context: A022690 A224332 A280478 * A105468 A125442 A260913

Adjacent sequences: A020924 A020925 A020926 * A020928 A020929 A020930

Keyword

sign

Author

N. J. A. Sloane

Status

approved